NOTATION xi
«?TR(X) space of continuous real-valued func-
tions on X with compact support: 13.2
/Z conjugate of the measure m 13.2
MR(X) space of real measures on X: 13.2
0t\ji, Jp real and imaginary parts of a complex
measure: 13.2
M+(X) set of positive measures on X: 13.3
/+,/~ positive and negative parts of a real-
valued function/: 13.3
jU^v order relation between real measures:
13.3
\\JL\ absolute value of a complex measure:
13.3
*/, ./(X) set of lower semicontinuous functions on
X which are bounded below by a function
belonging to JfR(X): 13.5
/<*(/), JV*. JVC*) *C*) upper integral of/: 13.5
J] tn sum of a sequence (ttt) of elements ^0 of
5: 13.5
£fy «^(X) set of upper semicontinuous functions on
X which are bounded above by a function
belonging to ^TR(X): 13.5
/**(/), J*/<fo J*/C*) <W*) lower integral of/: 13.5
jU*(A), /i*(A) outer and inner measures of A c X: 13.5
/ equivalence class of /(with respect to ^) :
13.6
f^g order relation between equivalence
classes: 13.6
f+$>f3 sum and product of equivalence classes :
13.6
)» </> /*> integral of a ju-integrable function: 13.7
J5fR(X, /i), J5fi(jw), jSf R space of (finite) real-valued /x-integrable
functions: 13.7
measure of a ju-integrable set: 13.7
integral of an equivalence class: 13.7
> JA/C*) *C*) integral of/ over A : 13.9
upper integral of /over A: 13.9
. measure induced by ju on a closed sub-
space Y: 13.9n the compact